Arguments over social policies often take place over superficial, concrete positions that don't really get at the positions of both sides. To this end: there's a feeling people often get that anti-abortion, anti-birth control "arguments" aren't really about protecting babies per se, but rather controlling women's reproductive freedom. (For example, male birth control is getting closer to reality and I haven't heard a single peep out of the usual concerned parties about that...)
So here's a thought experiment for you to find out what people are really after here. Let's make two changes to the world of our thought experiment. First, assume that there are medical discoveries made so that now, we can extract a fetus from a woman at any stage of development without harming the mother or the fetus - and have artificial wombs that can keep the fetus healthy and growing until "delivery" at 9 months. Second, assume that Bill Gates and Warren Buffett donate their every last cent to a fund to get adoptive parents to house, feed, clothe, raise and educate these kids, so they're taken care of after their artificial births. They'll have lives just like any other adopted baby.
If this became possible, would this be morally preferable to making women who don't want their baby carry the fetus to term? If not, why not?